Open Access

ARTICLE

Duffing Oscillator’s Vibration Control under Resonance with a Negative Velocity Feedback Control and Time Delay

by Y. A. Amer¹, Taher A. Bahnasy^2,*

1 Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt
2 Department of Engineering Physics and Mathematics, Faculty of Engineering, Tanta University, Tanta, Egypt

* Corresponding Authors: Taher A. Bahnasy. Email: ,

(This article belongs to the Special Issue: Analytical Methods for Nonlinear Vibration & Active Control in Nano/Micro Devices and Systems)

Sound & Vibration 2021, 55(3), 191-201. https://doi.org/10.32604/sv.2021.014358

Received 21 September 2020; Accepted 14 April 2021; Issue published 15 July 2021

Abstract

An externally excited Duffing oscillator under feedback control is discussed and analyzed under the worst resonance case. Multiple time scales method is applied for this system to find analytic solution with the existence and nonexistence of the time delay on control loop. An appropriate stability analysis is also performed and appropriate choices for the feedback gains and the time delay are found in order to reduce the amplitude peak. Different response curves are involved to show and compare controller effects. In addition, analytic solutions are compared with numerical approximation solutions using Rung-Kutta method of fourth order.

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